A329704 Numbers k such that the sum of divisors of k (A000203) and the sum of proper divisors of k (A001065) are both triangular numbers (A000217).

1, 2, 5, 36, 54, 441, 473, 6525, 52577, 124025, 683820, 1513754, 1920552, 6079931, 6762923, 14751657, 17052782, 17310942, 36543714, 49919939, 60260967, 251849052, 364535720, 372476909, 562047389, 670395564, 670440852, 783856979, 824626800, 1084201689, 1122603809

Offset

1,2

Comments

Are 1 and 36 the only terms that are also triangular numbers?

No other triangular terms up to A000217(10^8). - Michel Marcus, Mar 01 2020

Links

Amiram Eldar, Table of n, a(n) for n = 1..48

Example

5 is a term since sigma(5) = 6 and sigma(5) - 5 = 1 are both triangular numbers.

Mathematica

triQ[n_] := IntegerQ @ Sqrt[8*n+1]; Select[Range[10^5], triQ[(s = DivisorSigma[1, #])] && triQ[s - #] &]

Prog

(PARI) isok(k) = my(s=sigma(k)); ispolygonal(s, 3) && ispolygonal(s-k, 3); \\ Michel Marcus, Feb 29 2020

Crossrefs

Intersection of A045745 and A045746.

Cf. A000203, A000217, A001065.

Sequence in context: A309667 A059586 A160968 * A275552 A086832 A317801

Adjacent sequences: A329701 A329702 A329703 * A329705 A329706 A329707

Keyword

nonn

Author

Amiram Eldar, Feb 28 2020

Status

approved